...and mine altcoins with OC settings, right? I don't think warranty works in that situation.
What you basically say is that mining void warranty? And how can you know what exactly has happened to the GPU when it failed? Assuming that it had stock bios.
If the card has its stickers, no signs of tampering, radiator removal or water stains you should get a new one. I had a similar thing in Asus card but in my case one of the lines near memory chip burned. Tell us how it went. 
Gigabyte has such a bad customer service in Greece. I'll have to take my card to where bought it tomorrow. Any idea if burned capacitors fall in warranty? All I did was to plug my computer in... 